The question is a homework question about wait line analysis with P-K Formula. The solutions are with the question, but there are parts of the solution which is in red

Assume 8 people are enjoying a day at the amusement park and one of the attractions is the roller coaster that only has one card which can seat a group of four people. a ride will take exactly 1.5 minutes in the time for one group to get off in another group to get into the cart is fixed to 1.5 minutes so that everybody is on and off safely. on average a group of four park visitors arrives every 4 minutes at the roller coaster (Consider the most natural distributions for arrivals).

When do you know the system is exponentially distributed or deterministic (what do they mean)? Can a system only be something other than exponentially distributed or deterministic? Can Ca and Cs be a number other than 0 or 1?

c)If a group of 4 people wait for 4.5 minutes to take the ride,

The last sentence, "Thus in total...27$ per hour" doesn't make sense to me. What does 135 minute-guests mean? Please explain what $1 every 5 minute-guests means and why you do 135/5 as well.

Thanks

(a) Given arrival rate, service rate, coefficient of variation of interarrival time and coffe- cient of variation of service time with respect to this attraction. E[a] = 4 [min/groups), i.e., we have a "group" arriving every 4 minutes. So, arrival rate 1 = Eta = 1/4 [min/group]= 15 group/hr. Service time is 1.5 minutes for trip plus 1.5 minutes for getting on/off. Thus, E [s] = 3 minutes per group, and service rate u = Etg = 1/3 (min/group] = 20 group/hr. Ca = 1(We assume exponentially distributed, 4 min on average). Cs = 0 (deterministic: exactly, fixed). (c) How much money would the park visitors who want to take the roller coaster above spend in the park per hour if 50% of those are using FastPass? Assume that this park uses a similar virtual queuing system as Disney World's Fast- Pass. Further suppose that guests using FastPass can walk right on to the attraction without waiting, and that they spend $1 every 5 minutes that they roam about in the park instead of waiting in line. Per hour 15 groups arrive, thus, 60 guests arrive. 50% of those have a FastPass, i.e., 30 guests per hour can spend 4.5 min in the park buying drinks/snacks/souvenirs rather than standing in line. Thus in total 30(4.5) = 135 minute-guests. At $1 every 5 minute-guests, this results in 135/5 = 27$ per hour